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private fun readChar(): Char = readString()[0]
private fun readChars(): CharArray = readString().toCharArray()
private fun readInt(): Int = readLine()!!.toInt()
private fun readInts(): List<Int> = readLine()!!.trim().split(" ").map(String::toInt)
private fun readLong(): Long = readLine()!!.toLong()
private fun readLongs(): List<Long> = readLine()!!.trim().split(" ").map(String::toLong)
private fun readString(): String = readLine()!!.trim()
private fun readStrings(): List<String> = readLine()!!.trim().split(" ")
fun roll(die: Int, dieSides: Int) = Pair(die + (die % dieSides) + (die + 1) % dieSides + 2, (die + 2) % dieSides + 1)